Various medical conditions can be treated by way of radiation therapy. For example, some cancers can be treated by exposure to radiation. Modern methods attempt to deliver radiation dose distributions which are designed carefully to deliver radiation to desired locations while sparing surrounding tissues in a subject. Intensity modulated radiation therapy (IMRT) is one such method.
Radiation delivery apparatus can have a large number of degrees of freedom. Typical radiation delivery apparatus has a source of radiation, such as a linear accelerator and a rotatable gantry. The gantry can be rotated to cause radiation to be incident on a subject from different angles. The shape of the incident radiation beam can be modified by a multi-leaf collimator. The multi-leaf collimator has a number of leaves that are substantially opaque to radiation. The leaves can be advanced to block radiation in a portion of the beam or retracted to allow radiation to pass. The multi-leaf collimator may be rotated to different angles. Some modes of delivering radiation that make use of a rotatable multi-leaf collimator are described in Otto, U.S. Pat. No. 6,907,105, which is hereby incorporated by reference herein.
A radiation treatment plan for a subject typically specifies a three-dimensional distribution of radiation dose that it is desired to deliver to a target region within the subject. The desired dose distribution typically specifies dose values for voxels lying within the target. Ideally, no radiation would be delivered to tissues outside of the target. The goal in Intensity Modulated Radiation Therapy (IMRT) inverse planning is to generate a desired dose in the target while reducing the dose as much as possible to critical structures and healthy tissue.
After a desired dose distribution has been established, treatment planning is conventionally performed in two steps. First, fluence maps for a number of predetermined gantry angles are updated iteratively under the constraints of a cost function until a set of fluence maps that yields an optimal dose distribution is obtained. Second, field shapes that will generate the optimal fluence maps are generated using a leaf sequencing algorithm. Constraints imposed by the structure of a multi-leaf collimator (MLC) to be used in shaping the radiation are taken into account during the leaf sequencing step. Various aspects of this conventional approach to treatment planning are given in:                S. V. Spirou and C. S. Chui. A gradient inverse planning algorithm with dose-volume constraints, Med. Phys. 25, 321-333 (1998);        Q. Wu and R. Mohand. Algorithm and functionality of an intensity modulated radiotherapy optimization system, Med. Phys. 27, 701-711 (2000);        S. V. Spirou and C. S. Chui. Generation of arbitrary intensity profiles by dynamic jaws or multileaf collimators, Med. Phys. 21, 1031-1041 (1994);        P. Xia and L. J. Verhey. Multileaf collimator leaf sequencing algorithm for intensity modulated beams with multiple static segments, Med. Phys. 25, 1424-1434 (1998); and        K. Otto and B. G. Clark. Enhancement of IMRT delivery through MLC rotation,” Phys. Med. Biol. 47, 3997-4017 (2002).        
The degrees of freedom available in typical radiation treatment apparatus mean that, a given desired dose distribution can typically be achieved by applying any of a wide range of possible sequences of fields. There is a need for ways to identify an optimum, or nearly optimum, set of fields.